GenODA Structural Decomposition vs. Log-Linear Model of One-Step Markov Transition Data: Stability and Change in Male Geographic Mobility in 1944-1951 and 1951-1953

Paul R. Yarnold

Optimal Data Analysis, LLC

Prior research modeled one-step Markov transition data indicating geographic mobility of American males after WWII, across time, via log-linear analysis. Results revealed: “…most men stayed in their initial regions…but the observed values on the main diagonal are lower in the first matrix, suggesting that the geographic mobility process may not have remained constant over the full period. …Of course, with more than 26,000 cases involved, finding an acceptable fit for anything less than the saturated model is difficult” (p. 56). In this exposition the Gen algorithm is used to conduct structural decomposition analysis (SDA) to identify underlying structural patterns involving stable vs. changing geographic location over time.

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Novometrics vs. ODA vs. Log-Linear Model in Analysis of a Two-Wave Panel Design: Assessing Temporal Stability of Catholic Party Identification in the 1956-1960 SRC Panels

Paul R. Yarnold

Optimal Data Analysis, LLC

Prior research used the log-linear model to explain shifts in political party identification (democrat=1; independent=2; republican=3) of 202 Catholic voters who reported party identification in the 1956 and 1960 presidential elections. The results showed: “When the symmetry model is fitted to the six off-diagonal cells…L2=20.99, with df=3, which means we must reject the hypothesis that shifts in each direction tended to cancel each other. …Since 2=15.7 for df=1, we conclude that there is a significant tendency for net change to occur predominantly in one direction. Inspection of the table shows that to be in a Democratic direction. …For the quasi-symmetry hypothesis…L2 =0.12 and df=1. Thus we conclude that the panel data approach symmetry, given unequal marginals in the two years. …The difference in L2 between symmetry and quasi-symmetry models is 20.87 and the difference in df is 2. It is, therefore, reasonable to conclude that the marginal distribution of Catholic voter party identification differs significantly between 1956 and 1960” (pp. 51-54). Exploratory novometric analysis is used to model party identification in 1960 (multicategorical class variable) using party identification in 1956 (multicategorical attribute). Next ODA is used to evaluate temporal stability (confirmatory hypothesis) and to identify statistically reliable instability (exploratory hypothesis) underlying party identification assessed across time.

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Novometric Analysis vs. GenODA vs. Log-Linear Model: Temporal Stability of the Association of Presidential Vote Choice and Party Identification

Paul R. Yarnold

Optimal Data Analysis, LLC

Prior research modeled presidential vote (democrat=1; republican=2) as a function of political party identification (democrat=1; independent=2; republican=3) and time (1972=72; 1976=76) via nonsaturated log-linear analysis. Results revealed: “The model {TP}{TV}{PV} has L2=1.88 with df=2. Hence, the best-fitting log-linear model need not include the interaction effect, TPV, thus indicating no significant change in the PV relationship over time… The two bivariate relationships, TP and TV, have substantive interpretations. They indicate that it is the marginal distributions of the vote choice and party identification (within categories of the other variables) which change between times of measurement” (p. 48). Exposition first uses exploratory novometric analysis to model presidenial vote (binary class variable) as a function of political party identification (multicategorical attribute) and time (an ordered attribute). The GenODA algorithm is then used to assess the temporal stability (time is the Gen variable) of the relationship between presidential vote (class variable) and political party identification (categorical attribute).

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Novometric vs. Recursive Causal Analysis: The effect of Age, Education, and Region on Support of Civil Liberties

Paul R. Yarnold

Optimal Data Analysis, LLC

Prior research modeled support of another person’s civil liberties (“voted to disallow a Communist speaker”=0; “voted to allow the speaker”=1) as a function of arbitrarily parsed age (39 years=1); education (no college=0; college=1); and region (South, defined as all states in Census South and Border States=1; non-South=0) via log-linear analysis. Results revealed: “The recursive causal model which best represents the data… is the sum of the models for the successive two-, three-, and four-way crosstabulations. The model fits the marginal tables {A}{R}{AR}{RE}{AE}{RS} {AS}{ES} and has L2=3.71 with df=6. …Thus we can see that older persons tend to have lower education, while those living outside the South have a greater chance of some college experience. Odds on holding a tolerant civil liberties attitude are raised by college education and living outside the South but are lower among older persons” (p. 45). Exploratory novometric analysis is used to model support of another’s civil liberties (binary class variable) as a function of region (a categorical at¬tribute), education and age (both treated as ordered attributes measured on categorical ordinal scales).

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Novometrics vs. Yule’s Q: Voter Turnout and Organizational Membership

Paul R. Yarnold

Optimal Data Analysis, LLC

A popular legacy index of association for 2×2 tables that is based on the odds ratio (OR), Yule’s Q=(OR–1)/(OR+1). Yule’s Q ranges between -1.00 and 1.00, with the value 0 indicating no association. Prior research assessing the association between voting behavior (0=not a voter; 1= voter) and the number of one’s organizational memberships (0=no memberships; 1=at least one membership) reported that Q=0.434, and “…the odds of voting among persons belonging to organizations (is) more than 2.5 times greater than the voting odds among those respondents without memberships” (p. 11). These data were analyzed using exploratory novometrics, treating voting behavior as a class variable and number of organizational memberships as an ordered attribute.

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Novometric Analysis Predicting Voter Turnout: Race, Education, and Organizational Membership Status

Paul R. Yarnold

Optimal Data Analysis, LLC

Prior research modeled voter turnout (“not voted”=0; “voted”=1) as a function of race (“white”=1; “black”=2), education (“less than high school”=1; “high school graduate”=2; “college”=3), and memberships in organizations (“none”=0; “one or more”=1) via log-linear analysis. Results revealed: “…in the absence of a confirmatory analysis with another sample and in the absence of any compelling theoretical argument for expecting the particular three-variable interaction, (our own preference) would be to choose the more parsimonious model 28, {MER}{MV}{EV}. That model gives a satisfactory fit to the full crosstabulation (L2=4.76, df=5, p<0.45) without resort to a complex three-variable interaction. It also omits the race-turnout effect which is known to be trivial, but which would have to be included in model 34 because it is subsumed in hierarchical relation to the {ERV} term” (p. 40). Exploratory novometric analysis is used to model voter turnout (binary class variable) as a function of race (a categorical attribute), education and number of organizational memberships (both treated as ordered attributes measured on categorical ordinal scales).

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Comparing MMPI-2 F-K Index Normative Data among Male and Female Psychiatric and Head-Injured Patients, Individuals Seeking Disability Benefits, Police and Priest Job Applicants, and Substance Abusers

Paul R. Yarnold

Optimal Data Analysis, LLC

Used as a validity indicator with the MMPI-2, the F-K Index helps to identify people who may over- or under-report psychological issues. Prior research obtained normative data on this index for males and females sampled in a variety of settings, and visual examination of resulting score distributions suggested: “The F-K score distributions appear to differ across the different samples of diagnostic and job applicant samples, as the clinical profiles of these groups would be expected to differ from one another. …Thus, no single set of cutoff scores should be used to judge the motivation or validity of clinical profiles of subjects from different clinical or normative populations” (p. 9). Exploratory novometric analysis is used to predict F-K score as a function of gender and setting in order to establish the existence and assess the strength of the hypothesized inter-sample differences in F-K score distributions.

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